A circle with center (-1, 2) passes through point (2, -2). Which is true?
A) The circle has a radius of 5.
To solve this problem, we can use the distance formula to find the distance between the center of the circle (-1, 2) and the point on the circle (2, -2).
Distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((2 - (-1))^2 + (-2 - 2)^2)
d = sqrt(3^2 + (-4)^2)
d = sqrt(9 + 16)
d = sqrt(25)
d = 5
Therefore, the distance between the center of the circle and the point on the circle is 5. Since all points on the circle are equidistant from the center, the radius of the circle is 5.
Thus, (A) The circle has a radius of 5 is true.
To determine which statement is true, let's analyze the given information:
1. The circle has a center point at (-1, 2).
2. The circle passes through the point (2, -2).
We need to find the equation of the circle to determine which statement is true.
The general equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Using the given center coordinates (-1, 2), the equation becomes:
(x - (-1))^2 + (y - 2)^2 = r^2
(x + 1)^2 + (y - 2)^2 = r^2
Now, we can substitute the coordinates of the point (2, -2) into the equation and check which statement is true.
(2 + 1)^2 + (-2 - 2)^2 = r^2
3^2 + (-4)^2 = r^2
9 + 16 = r^2
25 = r^2
Therefore, the true statement is:
The circle has a radius of 5 units.